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Research Papers

A Velocity Predictor–Corrector Scheme in Level Set-Based Topology Optimization to Improve Computational Efficiency

[+] Author and Article Information
Benliang Zhu

Guangdong Province Key Laboratory of Precision
Equipment and Manufacturing Technology,
School of Mechanical
and Automotive Engineering,
South China University of Technology,
Guangzhou 510640, China
e-mail: lllang123@163.com

Xianmin Zhang

Professor
Guangdong Province Key Laboratory of Precision
Equipment and Manufacturing Technology,
School of Mechanical
and Automotive Engineering,
South China University of Technology,
Guangzhou 510640, China
e-mail: zhangxm@scut.edu.cn

Sergej Fatikow

Chair Professor
School of Mechanical
and Automotive Engineering,
South China University of Technology,
Guangzhou 510640, China
e-mail: fatikow@uni-oldenburg.de

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 30, 2013; final manuscript received May 13, 2014; published online June 11, 2014. Assoc. Editor: Kazuhiro Saitou.

J. Mech. Des 136(9), 091001 (Jun 11, 2014) (9 pages) Paper No: MD-13-1438; doi: 10.1115/1.4027720 History: Received September 30, 2013; Revised May 13, 2014

This paper presents an optimization method for solving level set-based topology optimization problems. A predictor–corrector scheme for constructing the velocity field is developed. In this method, after the velocity fields in the first two iterations are calculated using the shape sensitivity analysis, the subsequent velocity fields are constructed based on those obtained from the first two iterations. To ensure stability, the velocity field is renewed based on the shape sensitivity analysis after a certain number of iterations. The validity of the proposed method is tested on the mean compliance minimization problem and the compliant mechanisms synthesis problem. This method is quantitatively compared with other methods, such as the standard level set method, the solid isotropic microstructure with penalization (SIMP) method, and the discrete level set method.

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Figures

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Fig. 1

The design domain of (a) the minimum compliance topology optimization problem and (b) compliant mechanisms topology optimization problem

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Fig. 2

The relationship between Vn2 and Vn1 for a one-dimensional problem

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Fig. 3

The design domain of the bridge topology optimization problem

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Fig. 4

The initial design of the bridge problem which is used both in the proposed method and TOPLSM 199

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Fig. 5

The final designs of the bridge problem that are obtained by using: (a) the proposed method, (b) the TOPLSM 199, (c) the discrete level set method, and (d) the SIMP method

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Fig. 6

The convergence histories of the structure obtained using the proposed method and the discrete level set method

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Fig. 7

The value of α in different iteration steps

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Fig. 8

The designs of the bridge problem obtained after one design cycle by using the proposed method with different rf: (a) rf = 10, (b) rf = 20, (c) rf = 30, and (d) rf = 40(min(nelx, nely))

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Fig. 9

The velocity field errors corresponding to Fig. 8: (a) rf = 10, (b) rf = 20, (c) rf = 30, and (d) rf = 40 (min(nelx, nely))

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Fig. 10

The design domain of the displacement inverter topology optimization problem

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Fig. 11

The initial design of the displacement inverter

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Fig. 12

The final designs of the displacement inverter obtained using the conventional level set method (a) and the proposed method (b)

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Fig. 13

The convergence histories of the displacement inverter problem obtained by using the proposed and the standard level set method

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Fig. 14

The effect of initial design on the topology optimization of displacement inverter: (a) case 1, and (b) case 2

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